Problem: Express your answer as a mixed number simplified to lowest terms. $19\dfrac{1}{5}-16\dfrac{7}{11} = {?}$
Find a common denominator for the fractions: $= {19\dfrac{11}{55}}-{16\dfrac{35}{55}}$ Convert ${19\dfrac{11}{55}}$ to ${18 + \dfrac{55}{55} + \dfrac{11}{55}}$ So the problem becomes: ${18\dfrac{66}{55}}-{16\dfrac{35}{55}}$ Separate the whole numbers from the fractional parts: $= {18} + {\dfrac{66}{55}} - {16} - {\dfrac{35}{55}}$ Bring the whole numbers together and the fractions together: $= {18} - {16} + {\dfrac{66}{55}} - {\dfrac{35}{55}}$ Subtract the whole numbers: $=2 + {\dfrac{66}{55}} - {\dfrac{35}{55}}$ Subtract the fractions: $= 2+\dfrac{31}{55}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{31}{55}$